Lent or No Lent, Life is War

By John Piper
Desiring God Blog

Lent or no Lent, not doing some things you feel like doing is the daily pattern for the disciples of Jesus. Yes, daily. “If anyone would come after me, let him deny himself and take up his cross daily and follow me” (Luke 9:23).

In the resurrection there will be no self-denial because none of our desires will be sinful or foolish. Till then we have sinful and foolish desires daily. Hence, “Let him deny himself and take up his cross daily.”

What Paul Says

This is so essential in Christian living that Paul made it part of his one-time sermon to Felix (“he reasoned about righteousness and self-control and the coming judgment,” Acts 24:25); he made it part of the fruit of the Spirit (“faithfulness, gentleness, self-control,” Galatians 5:23); he made it part of the qualifications for overseers (“self-controlled, upright, holy, and disciplined,” Titus 1:8).

And he gave us a taste of the sort of thing he meant: “But if they cannot exercise self-control, they should marry” (1 Corinthians 7:9). So he means there are times for denying some of the desires we have for sex.

It’s the sort of thing that athletes do. “Every athlete exercises self-control in all things” (1 Corinthians 9:25). Paul had very little trust in the desires his body threw at him daily: “I discipline my body and keep it under control, lest after preaching to others I myself should be disqualified” (1 Corinthians 9:27). That’s an innocuous translation. Literally: “I give my body a black eye (hupopiazō) and make it a slave (doulagōgō).”

The Christian Experience

This is normal, daily, Christian warfare. Only saints delight in the law of God at their depths. Here is how they talk: “I find it to be a law that when I want to do right, evil lies close at hand. For I delight in the law of God, in my inner being, but I see in my members another law waging war against the law of my mind” (Romans 7:21–23).

A war indeed. Daily. “The desires of the flesh are against the Spirit, and the desires of the Spirit are against the flesh, for these are opposed to each other, to keep you from doing the things you want to do” (Galatians 5:17).

And make no mistake, sexual desires are not our most deadly desires that need daily denial. Anger, resentment, fear of man, discouragement (yes), self-pity, self-promotion, hardness, envy, moodiness, sulking, indifference to suffering, laziness, boredom, passiveness, lack of praise, lack of joy in Jesus, disinterest in others, etc. These need daily killing (Romans 8:13).

Is this Christian Hedonism? Yes. Why does Paul live like a self-disciplined athlete? Simple: Greater joy. “Every athlete exercises self-control in all things. They do it to receive a perishable wreath, but we an imperishable” (1 Corinthians 9:25).

Is God Glad Osama Bin Laden's Dead?

By John Piper
Desiring God Blog

God’s emotions are complex—like yours, only a million times more. Right now, your emotions about bin Laden are not simple, i.e. not single. There are several, and they intermingle. That is a good thing. You are God-like.

In response to Osama bin Laden’s death, quite a few tweets and blogs have cited the biblical truth that “God does not delight in the death of the wicked.” That is true.

It is also true that God does delight in the death of the wicked. There are things about every death that God approves in themselves and things about every death that God disapproves in themselves.

Is God Double-Minded?

This is not double talk. All thoughtful people make such distinctions. For example, if my daughter asks me if I like a movie, I might say yes or no to the same movie. Why? Because a movie can be assessed for its 1) acting, 2) plot, 3) cinematography, 4) nudity, 5) profanity, 6) suspense, 7) complexity, 8) faithfulness to the source, 9) reverence for God, 10) accurate picture of human nature, etc., etc., etc.

So my answer is almost always “yes, in some ways, and no in other ways.” But sometimes I will simply say yes, and sometimes no, because of extenuating circumstances.

Here is why I say God approves and disapproves the death of Osama bin Laden:

In one sense, human death is not God’s pleasure:

Have I any pleasure in the death of the wicked, declares the Lord God, and not rather that he should turn from his way and live? . . . For I do not pleasure in the death of anyone, declares the Lord God; so turn, and live. (Ezekiel 18:23, 32).

In another sense, the death and judgment of the unrepentant is God’s pleasure:

Thus shall my anger spend itself, and I will vent my fury upon them and satisfy myself. (Ezekiel 5:13]

[Wisdom calls out:] Because you have ignored all my counsel and would have none of my reproof, I also will laugh at your calamity; I will mock when terror strikes you. (Proverbs 1:25–26)

Rejoice over her, O heaven, and you saints and apostles and prophets, for God has given judgment for you against her! (Revelation 18:20)

As the Lord took delight in doing you good . . . so the Lord will take delight in bringing ruin upon you and destroying you. (Deuteronomy 28:63)

We should not cancel out any of these passages but think our way through to how they can all be true.

God is Not Malicious or Bloodthirsty

My suggestion is that the death and misery of the unrepentant is in and of itself not a pleasure to God. God is not a sadist. He is not malicious or bloodthirsty. The death and suffering considered for itself alone is not his delight.

Rather, when a rebellious, wicked, unbelieving person is judged, what God has pleasure in is the exaltation of truth and righteousness, and the vindication of his own honor and glory. (For further discussion of God’s heart in judgment see the section in The Pleasures of God called “How Is God Like George Washington?”, pp. 147–149.)

When Moses warns Israel that the Lord will take pleasure in bringing ruin upon them and destroying them if they do not repent (Deuteronomy 28:63), he means that those who have rebelled against the Lord and moved beyond repentance will not be able to gloat that they have made the Almighty miserable.

God is not defeated in the triumphs of his righteous judgment. Quite the contrary. Moses says that when they are judged they will unwittingly provide an occasion for God to rejoice in the demonstration of his justice and his power and the infinite worth of his glory (see also Romans 9:22–23).

A Warning

Let this be a warning to us: God is not mocked. He is not trapped or cornered or coerced. Even on the way to Calvary he had legions of angels at his disposal: “No one takes my life from me; I lay it down of my own accord”—of his own good pleasure, for the joy that was set before him.

At the one point in the history of the universe where God looked trapped, he was in charge, doing precisely what he pleased—dying to justify the ungodly like you and me.

(Adapted from The Pleasures of God, 66-74.)

The Sovereign God of “Elfland” (Why Chesterton’s Anti-Calvinism Doesn’t Put Me Off)

By John Piper
Desiring God Blog

Ever since my days at Wheaton College, when I followed Clyde Kilby’s advice to read G. K. Chesterton’s Orthodoxy, it has been one of my favorite books. I think it’s the only book I have read more than twice (except for the Bible).

This is strange. Not only was Chesterton a Roman Catholic, he also hated Calvinism. So what’s up with me and Orthodoxy? I still think at least half a dozen Roman Catholic distinctives are harmful to true Christian faith (e.g., papal authority, baptismal regeneration, transubstantiation, justification as impartation, purgatory, the veneration of Mary). And I think “the doctrines of grace” (“Reformed theology,” “Calvinism”) are a precious and healthy expression of biblical doctrine.

Common Ground (“Elfland”)

But I keep coming back to Chesterton’s Orthodoxy. The reason is that we see the world so similarly, and the Calvinism he hates is not the Calvinism I love.

• We both marvel that we are swimming in the same boundless sea of wonders called the universe.

• We both are amazed not by sharp noses or flat noses, but that humans have noses at all.

• We both think it is just as likely that the reason the sun rises every morning is not because of some so-called “law,” but because God says, “Do it again.” And that he says it more like a delighted child than a dour chief.

• We both believe logic and imagination are totally compatible and that neither will be useful without the other.

• We both believe that the magic of the universe must have meaning, and meaning must have someone to mean it.

• We both believe that the glories of this world are like goods rescued from some primordial ruin — a ruin whose evidences are everywhere.

• And we both believe that paradox is woven into the nature of the universe, and that resisting it drives a person mad. “Poets don’t go mad; but chess-players do. Mathematicians go mad, and cashiers; but creative artists very seldom. . . . The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits.”

These and a hundred other happy, world-opening agreements keep me coming back, because nobody says them better than Chesterton. Like C. S. Lewis, he sees more wonder in an ordinary day than most of us see in a hundred miracles. I will keep coming back to anyone who helps me see and be astonished at what is in front of my face — anyone who can help heal me from the disease of “seeing they do not see.”

Not the Same Calvinism

But how then can Calvinism awaken such joy in me, and such hate in Chesterton? Because they aren’t the same Calvinism. He thinks Calvinism is the opposite of all this happy wonder that we have in common. The Calvinism he hates is part of the rationalism that drives people mad. Exhibit A:

Only one great English poet went mad, Cowper. And he was definitely driven mad by logic, by the ugly and alien logic of predestination. Poetry was not the disease, but the medicine; poetry partly kept him in health. . . . He was damned by John Calvin; he was almost saved by John Gilpin.

No, Mr. Chesterton, William Cowper was not driven mad by Calvinism. He was driven mad by a mental disease that ran in his family for generations, and he was saved by John Newton, perhaps the humblest, happiest Calvinist who ever lived. And both of them saw the wonders of “Amazing Grace” through the eyes of poetry. Yes, that was a healing balm. But the disease was not Calvinism — else John Newton would not have been the happy, healthy, holy friend that he was.

The Calvinism that Grows in “Elfland”

Here’s the reason Chesterton’s bowshots at Calvinism do not bring me down. The Calvinism I love is far closer to the “Elfland” he loves than the rationalism he hates.

He would no doubt be baffled by my experience. For me the biggest, strongest, most beautiful, and most fruitful tree that grows in the soil of “Elfland” is Calvinism. Here is a tree big enough, and strong enough, and high enough to let all the paradoxical branches of the Bible live — and wave with joy in the sunshine of God’s sovereignty.

In the shade of this tree, I was set free from the procrustean forces of unbiblical, free-will presuppositionalism — the unyielding, alien assumption that without the human right of ultimate self-determination human beings cannot be accountable for their choices. When I walked away from this narrow, rationalistic, sparse tree, into the shade of the massive tree of Calvinism, it was a happy day. Suddenly I saw that this is what all the poetry had been about. This is the tree where all the branches of all the truths that men have tried to separate thrive.

What About Logic?

It is a great irony to me that Calvinists are stereotyped as logic-driven. For forty years my experience has been the opposite. The Calvinists I have known (English Puritans, Edwards, Newton, Spurgeon, Packer, Sproul) are not logic driven, but Bible-driven. It’s the challengers who bring their logic to the Bible and nullify text after text. Branches are lopped off by “logic,” not exegesis.

Who are the great enjoyers of paradox today? Who are the pastors and theologians who grab both horns of every biblical dilemma and swear to the God-Man: I will never let go of either.

Not the Calvinism-critics that I meet. They read of divine love, and say that predestination cannot be. They read of human choice and say the divine rule of all our steps cannot be. They read of human resistance, and say that irresistible grace cannot be. Who is logic-driven?

For forty years Calvinism has been, for me, a vision of life that embraces mystery more than any vision I know. It is not logic-driven. It is driven by a vision of the ineffable, galactic vastness of God’s Word.

Let’s be clear: It does not embrace contradiction. Chesterton and I both agree that true logic is the law of “Elfland.” “If the Ugly Sisters are older than Cinderella, it is (in an iron and awful sense) necessary that Cinderella is younger than the Ugly Sisters.” Neither God nor his word is self-contradictory. But paradoxes? Yes.

We happy Calvinists don’t claim to get the heavens into our heads. We try to get our heads into the heavens. We don’t claim comprehensive answers to revealed paradoxes. We believe. We try to understand. And we break out into song and poetry again and again.

From Dilemma to Unicorn

We don’t adjust the brain-baffling categories of Scripture to fit human reason. We take it as one of our jobs to create categories in human minds that never existed in those minds before — a job only God can do — though he makes us agents. For example, we labor to create categories of thought like these:

• God rules the world of bliss and suffering and sin, right down to the roll of the dice, and the fall of a bird, and the driving of the nail into the hand of his Son; yet, even though he wills that such sin and suffering be, he does not sin, but is perfectly holy.

• God governs all the steps of all people, both good and bad, at all times and in all places; yet such that all are accountable before him and will bear the just consequences of his wrath if they do not believe in Christ.

• All people are dead in their trespasses and sins, and are not morally able to come to Christ because of their rebellion; yet, they are responsible to come, and will be justly punished if they don’t.

• Jesus Christ is one person with two natures, divine and human, such that he upheld the world by the word of his power while living in his mother’s womb.

• Sin, though committed by a finite person and in the confines of finite time is nevertheless deserving of an infinitely long punishment because it is a sin against an infinitely worthy God.

• The death of the one God-Man, Jesus Christ, so displayed and glorified the righteousness of God that God is not unrighteous to declare righteous ungodly people who simply believe in Christ.

These are some of the intertwining, paradoxical branches in the tree of Calvinism. They do not grow in the soil of fallen human logic. They grow in the Bible-saturated soil of “Elfland.” Those who live there believe that a Dilemma with two horns is probably metamorphosing into a Unicorn.

I thank God for G. K. Chesterton. His gift for seeing the world and for saying what he sees is peerless. He opens my eyes to wonders of what is there. And what is there is the finger-work of God. He may be dismayed to hear it, but his eyes have helped me see more clearly than ever the God of Jonathan Edwards.

Today John Hooper was Burned (1555)

By Fred Sanders
Scriptorium Daily

They burned him at the stake, and he knew it was coming. John Hooper (born around 1500 – martyred February 9, 1555) was the bishop of Gloucester in the sixteenth century. When the Church of England pendulum swung back towards Roman Catholicism under Mary, Hooper was predictably high on the list of people who would have to die: He was outspoken, politically engaged, inflexibly conscientious, and very very Protestant.

He was so Protestant that he objected to some of Calvin’s early writings. He was so Protestant that only Bishop Ridley could perform his ordination service, and even he had trouble making the service and vows low-church enough to be permissible to Hooper. He was so Protestant that he strongly objected to ministers wearing priestly clothing in church: he called them Aaronic, Old Covenant symbols inappropriate for New Covenant ministry. Hooper argued his side of this first wave of the “vestment controversy” vigorously. He was so Protestant that it was the nonconformists and puritans would keep his works in circulation after his death.

Was Hooper too stubborn? Did he draw lines that didn’t need to be drawn, arguing over clothing? It’s a question worth investigating, but perhaps a bit tacky to ask such questions lightly of a genuinely Christian man who paid the full price for his convictions.

When the Catholic Mary Tudor came to power, it was only a matter of time before Hooper was imprisoned and executed.

One of Hooper’s most famous writings was a translation of Tertullian’s book To His Wife. But Hooper also had a wife, Anne, and he once wrote a letter to her reflecting on how to respond to the inevitable persecution. You might expect to learn a lesson from Hooper on the cost of obedience, but he was characteristically far more concerned about the cost of disobedience: He knew that disobedience came at the cost of a hardened heart and a reprobate mind. Here is the opening paragraph, a stately blast of Christian realism from a man who sealed his testimony with his death.

Our Saviour Jesus Christ, dearly beloved and my godly wife, in St Matthew’s gospel said to his disciples, that it was necessary slanders should come: and that they could not be avoided, he perceived as well by the condition of those that should perish and be lost for ever in the world to come, as also by their affliction that should be saved. For he saw the greatest part of the people would contemn and neglect whatsoever true doctrine or godly ways should be shewed unto them, or else receive it and use it as they thought good, to serve their pleasures, without any profit to their souls at all, not caring whether they lived as they were commanded by God’s word or not; but would think it sufficient to be counted to have the name of a Christian man, with such works and fruits of his profession and Christianity as his fathers and elders, after their custom and manner, esteem and take to be good fruits and faithful works, and will not try them by the word of God at all. These men, by the just judgment of God, be delivered unto the craft and subtilty of the devil, that they may be kept by one slanderous stumbling-block or other, that they never come unto Christ, who came to save those that were lost: as ye may see how God delivereth wicked men up unto their own lusts, to do one mischief after another, careless until they come into a reprobate mind, that forgetteth itself, and cannot know what is expedient to be done, or to be left undone, because they close their eyes, and will not see the light of God’s word offered unto them ; and being thus blinded, they prefer their own vanities before the truth of God’s word. Where as such corrupt minds be, there is also corrupt election and choice of God’s honour: so that the mind of man taketh falsehood for truth, superstition for true religion, death for life, damnation for salvation, hell for heaven, and persecution of Christ’s members for God’s service and honour.

Later, after some biblical exposition, he adds: “But these things, my godly wife, require rather cogitation, meditation, and prayer, than words or talk. They be easy to be spoken of, but not so easy to be used and practised.” Hooper’s letter is a classic short text, well worth reading.

John 3:16

By Fred Sanders
Scriptorium Daily

It’s one of the most famous verses in the Bible, the hit single everybody knows even if they don’t listen to the rest of the album. You can wave it on a banner, paint it in your eyeblack, or print it underneath your In-N-Out cup; John 3:16. No matter how often I see it, no matter what kind of knuckle-head has stuck it to their bumper, no matter how out-of-the-blue or isolated it is from its context, it always gets me.

Focus on the Family put it in the mouths of children and bought air time where a mass audience sensitized by Tebow hoopla would see and hear it. “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.”

This verse has everything.

Start with the little word “so.” It’s actually the first word in the sentence, at least in the original Greek of John 3:16. It’s a great big pointer word. Its primary meaning isn’t “so much,” but “in this way,” or “thus.” The verse doesn’t say “God loves the world so much that he sent his Son,” rather it says “Look at this, this right here is the way God loved the world: he sent his Son.”

God loved like this! As a pointer-word, “so” directs your attention like an index finger toward a thing so unparalleled and singular that all we can do it look and learn. And it points to a past action, an event already accomplished. Think how much we lose when we unconsciously simplify this verse down to “How much God loves the world” (present tense, emphasizing magnitude) rather than what it wants to show us: Right over here is how God did decisively love the world!

If you do follow the pointing word to the recommended object of attention, you see vast expanses of doctrine opening up in front of you. God is in action here: He loves, he gives, he saves the perishing. J. Sidlow Baxter wrote a whole book on this verse, published under the title The Best Word Ever (and released in America as God So Loved). Baxter noted that this Best Word Ever contains at least ten vocabulary words which could practically stock a Christian understanding with everything it needs. Just look at them isolated in Baxter’s list form:

(1) God
(2) Loved
(3) the World
(4) Gave/Gave Over
(5) Son
(6) whoever
(7) Believe/have faith
(8) Perish
(9) To Have/ Possess
(10) Life

It would be worthwhile to expound on the biblical meaning of each of those words, but I would like to do something else: show how John 3:16 carries an entire systematic theology within itself, implicitly.

Consider the doctrinal loci in a traditional order:

The Doctrine of Revelation: According to John 3:16, God has made this love known to us in a mighty act of salvation which we should pay attention to. In John 3, Jesus has just told Nicodemus that he has heavenly things to declare, because he is the one who has descended from heaven and gives testimony about what he knows for certain and has seen. One of the heavenly things made known in John 3:16 is that God has an only Son, which is big news. And he has made this known especially in Scripture, which brings us to…

The Doctrine of Scripture: Jesus is arguing from Scripture, citing the book of Numbers (“as Moses lifted up the serpent in the wilderness, so must the Son of Man be lifted up”), affirming the unity of Old and New Testaments, and implying with regard to the Old Testament its historical veracity and its openness to typological interpretation. There’s something here to offend everybody, so take your pick. To top it off, have you ever noticed that it’s not clear who is the speaker in John 3:16? Translations all offer their best guess about where the quotation marks should begin and end in this conversation with Nicodemus. Jesus may well be the speaker, but the narrator of the Gospel may also be intruding his voice here (as he does elsewhere). You may object that it doesn’t matter who is speaking, and you may be right. But the only way you’re right is if the voice of God sounds forth equally in the words of Jesus as in the words of his apostolic evangelist, if “what the Scriptures say, God says.”

The Doctrine of God: The message of the verse is about the universal love of God for the cosmos, which only makes sense with a strong doctrine of creation in place (insert an implied doctrine of creation here). This God is an intervener, a wonder-worker, a healer of his chosen people. He is a judge whose wrath threatens destruction, and a savior whose love brings life that has no limit short of eternity. Eternity is his. He is also the kind of God who has a unique Son, meaning he is God the Father –not “father” with relation to a world which is his offspring, but Father with relation to a Son who is unique, only-begotten (whether the word “monogenes” is best rendered that way or not), and so intimate to the Father’s being that he is give-able. Like all the best Christian theology, John 3:16?s doctrine of God leads inexorably to…

The Doctrine of Christ: In systematic theology, it is traditional to divide the doctrine of Christology into two major sections: 1. On the Person of Christ, and 2. On the Work of Christ. John 3:16 includes both. It teaches that Christ is the unique Son of God (that is his person) and that he is given for the life of the world (that is his work).

The Doctrine of Sin: Within 3:16 itself, a very dark shadow is cast by the “giving” of the Son which is parallel to the lifting up of the bronze serpent in the wilderness. What human situation is presupposed by this giving and this lifting up? If this is the solution, what must be the problem? The answer is sin. And the following verses make the nature of sin an explicit subject of description: “This is the judgment: the light has come into the world, and people loved the darkness rather than the light because their works were evil. For everyone who does wicked things hates the light and does not come to the light, lest his works should be exposed.” Sin is a particular kind of culpable ignorance, a suppressing of the truth by those who know better because they know where the light is and what it will show.

The Doctrine of Salvation: In this verse, it’s wall to wall soteriology (the doctrine about salvation). The Father and the Son have worked out the way of salvation, and it is a plan wherein people will be saved by looking up. Just as the serpent in the wilderness was lifted up, Jesus Christ will be lifted up and we will look to him and be rescued. Somewhere in the tension between the universal scope of “the world” and the particular results among “whosoever,” salvation reaches the chosen. It reaches them by faith in the Son, and it has the character of life. Look how God loved!

The Doctrine of The Church: If the previous doctrine was too easy to find because it is so pervasive, this one is hidden or absent. I just can’t find much ecclesiology in John 3:16. If you find some, send it to me. No fair importing the ecclesiology of the whole book of John.

The Doctrine of the Holy Spirit: The only way to find pneumatology in John 3:16 is to dig in your heels and swear that it’s hidden in the word “believe.” Doctrinally speaking, I would in fact insist that saving faith is only possible where the Holy Spirit is at work within the believer. But exegetically, even I am willing to rein in my interpretive acrobatics at this point. It cannot be insignificant, however, that John 3:16 is prefaced by Jesus’ admonition that “what is born of the flesh is flesh, but what is born of the Spirit is spirit,” and that ending the section we have the remarkable statement: “He whom God has sent utters the words of God, for he gives the Spirit without measure. The Father loves the Son and has given all things into his hand.”

The Doctrine of Final Things: Eschatology is here in John 3:16?s stark alternative between perishing and having eternal life. These are final and irreconcilable. Another kind of eschatology is recognized in the past tense of the verbs “loved” and “sent,” which show that God has already acted decisively and finally to bring about salvation. Between those accomplished past tenses of God’s determinative action on the one hand, and on the other hand the future tense of the life which believers will have and which those who perish will not have, we have the present moment when Jesus is telling Nicodemus that he must be born again.

(This is a revision of ScriptoriumDaily post from 2007.)

First Inaugural Address

By Andrew Jackson
TeachingAmericanHistory.org

Fellow-Citizens:

About to undertake the arduous duties that I have been appointed to perform by the choice of a free people, I avail myself of this customary and solemn occasion to express the gratitude which their confidence inspires and to acknowledge the accountability which my situation enjoins. While the magnitude of their interests convinces me that no thanks can be adequate to the honor they have conferred, it admonishes me that the best return I can make is the zealous dedication of my humble abilities to their service and their good.

As the instrument of the Federal Constitution it will devolve on me for a stated period to execute the laws of the United States, to superintend their foreign and their confederate relations, to manage their revenue, to command their forces, and, by communications to the Legislature, to watch over and to promote their interests generally. And the principles of action by which I shall endeavor to accomplish this circle of duties it is now proper for me briefly to explain.

In administering the laws of Congress I shall keep steadily in view the limitations as well as the extent of the Executive power, trusting thereby to discharge the functions of my office without transcending its authority. With foreign nations it will be my study to preserve peace and to cultivate friendship on fair and honorable terms, and in the adjustment of any differences that may exist or arise to exhibit the forbearance becoming a powerful nation rather than the sensibility belonging to a gallant people.

In such measures as I may be called on to pursue in regard to the rights of the separate States I hope to be animated by a proper respect for those sovereign members of our Union, taking care not to confound the powers they have reserved to themselves with those they have granted to the Confederacy.

The management of the public revenue--that searching operation in all governments--is among the most delicate and important trusts in ours, and it will, of course, demand no inconsiderable share of my official solicitude. Under every aspect in which it can be considered it would appear that advantage must result from the observance of a strict and faithful economy. This I shall aim at the more anxiously both because it will facilitate the extinguishment of the national debt, the unnecessary duration of which is incompatible with real independence, and because it will counteract that tendency to public and private profligacy which a profuse expenditure of money by the Government is but too apt to engender. Powerful auxiliaries to the attainment of this desirable end are to be found in the regulations provided by the wisdom of Congress for the specific appropriation of public money and the prompt accountability of public officers.

With regard to a proper selection of the subjects of impost with a view to revenue, it would seem to me that the spirit of equity, caution, and compromise in which the Constitution was formed requires that the great interests of agriculture, commerce, and manufactures should be equally favored, and that perhaps the only exception to this rule should consist in the peculiar encouragement of any products of either of them that may be found essential to our national independence.

Internal improvement and the diffusion of knowledge, so far as they can be promoted by the constitutional acts of the Federal Government, are of high importance.

Considering standing armies as dangerous to free governments in time of peace, I shall not seek to enlarge our present establishment, nor disregard that salutary lesson of political experience which teaches that the military should be held subordinate to the civil power. The gradual increase of our Navy, whose flag has displayed in distant climes our skill in navigation and our fame in arms; the preservation of our forts, arsenals, and dockyards, and the introduction of progressive improvements in the discipline and science of both branches of our military service are so plainly prescribed by prudence that I should be excused for omitting their mention sooner than for enlarging on their importance. But the bulwark of our defense is the national militia, which in the present state of our intelligence and population must render us invincible. As long as our Government is administered for the good of the people, and is regulated by their will; as long as it secures to us the rights of person and of property, liberty of conscience and of the press, it will be worth defending; and so long as it is worth defending a patriotic militia will cover it with an impenetrable aegis. Partial injuries and occasional mortifications we may be subjected to, but a million of armed freemen, possessed of the means of war, can never be conquered by a foreign foe. To any just system, therefore, calculated to strengthen this natural safeguard of the country I shall cheerfully lend all the aid in my power.

It will be my sincere and constant desire to observe toward the Indian tribes within our limits a just and liberal policy, and to give that humane and considerate attention to their rights and their wants which is consistent with the habits of our Government and the feelings of our people.

The recent demonstration of public sentiment inscribes on the list of Executive duties, in characters too legible to be overlooked, the task of reform, which will require particularly the correction of those abuses that have brought the patronage of the Federal Government into conflict with the freedom of elections, and the counteraction of those causes which have disturbed the rightful course of appointment and have placed or continued power in unfaithful or incompetent hands.

In the performance of a task thus generally delineated I shall endeavor to select men whose diligence and talents will insure in their respective stations able and faithful cooperation, depending for the advancement of the public service more on the integrity and zeal of the public officers than on their numbers.

A diffidence, perhaps too just, in my own qualifications will teach me to look with reverence to the examples of public virtue left by my illustrious predecessors, and with veneration to the lights that flow from the mind that founded and the mind that reformed our system. The same diffidence induces me to hope for instruction and aid from the coordinate branches of the Government, and for the indulgence and support of my fellow-citizens generally. And a firm reliance on the goodness of that Power whose providence mercifully protected our national infancy, and has since upheld our liberties in various vicissitudes, encourages me to offer up my ardent supplications that He will continue to make our beloved country the object of His divine care and gracious benediction.

The mathematics of your next family reunion

By Jeffrey Rosenthal
+ plus Magazine

– I am your father’s brother’s nephew’s cousin’s former roommate.
– What does that make us?
– Absolutely nothing!

(Lord Dark Helmet and Lone Starr, discussing family relationships in the Mel Brooks movie Spaceballs.)

Why is your great-grandmother great?

Keeping track of family relations can be difficult. If Edna marries your mother’s uncle Charlie, what should you call her? If your father’s cousin’s daughter just had a baby boy, how should you two be introduced? Who is your “great great aunt”, and how can you find your “first cousin twice removed”? Fortunately, a bit of mathematical logic can clarify who should be called what, and why – and even measure the degree of genetic similarity between different relatives.

Ancestor Lineage

To begin at the beginning (well, your beginning, anyway), you surely had two parents, a mother and father:

Continuing backwards, they each had two parents, giving you a total of four grandparents:

Going back still further, each of your ancestors in turn had two parents, indicated by prepending an extra “great” each time. For example, your maternal lineage is:

and so on (and similarly for “fathers” instead of “mothers” at any level).

Since each ancestor has two parents (one mother and one father), you have a total of 2n ancestors at level n: two parents, four grandparents, eight great-grandparents, sixteen great-great-grandparents, and so on. Summing up, you have a total of 2+2² +2³ +...+2ⁿ =2ⁿ⁺¹ − 2 ancestors of level n or lower; for example, your total number of parents and grandparents and great-grandparents combined is 2³⁺¹ − 2 = 16 − 2 = 14. In short, your ancestors form a perfect binary tree – simplicity itself.

Descendant legacy

If you have children yourself, then their children are your grandchildren, and your grand-children’s children are your great-grandchildren, and so on:

(and similarly for “son” instead of “daughter” at any level).

Unlike with ancestors, there is no simple formula for your number of descendants. Rather, you have to count up all of your children, and all of their children, and so on. For example, even if you have five children, it is possible that none of them will have children of their own, in which case your number of grandchildren will be zero. On the other hand, if they each have five children of their own, then you will have twenty-five grandchildren – a lot more.

Sideways, march!

When people have more than one child, this fattens the family tree, creating new relationships like sister and niece and great-aunt and more. For starters, if your parents have additional children besides you, then they are of course your siblings, that is your sisters and brothers:

(Here, and throughout, relationships to “you” are written within the boxes, and relationships between other pairs of individuals are indicated by connecting lines.)

If you and your siblings each have children, then those children are first-cousins of each other. Then, if the two first-cousins each have children, then those children are second-cousins of each other; and their children are third-cousins, and so on:

(and similarly for “son” instead of “daughter” at any level).

In general, n-level cousins share two (n + 1)-level ancestors (but no n-level ancestors). Thus, first-cousins share two grandparents (but no parents), and second-cousins share two great-grandparents (but no grandparents), and so on.

It follows that if A and B are n-level cousins, then A’s child and B’s child are (n+1)-level cousins. Thus, children of first-cousins are second-cousins, and children of second-cousins are third-cousins, and so on. In fact, if we regard siblings as 0-level cousins, then this reasoning applies to siblings too: children of 0-level cousins (ie, siblings) are themselves first-cousins.

Finally, your sibling’s child is your niece (or nephew, if male), and their child is your great-niece (or great-nephew), and so on:

(and similarly for “nephew” instead of “niece” at any level).

Cry Uncle

So now we know where your descendants’ cousins come from. To see where your cousins come from, we have to move up to your parents’ level. Your parents’ siblings are your aunts and uncles, and their children are your first-cousins (since you and they share the same grandparents, but not the same parents):

If your cousins have children, then what are they to you? Well, children of your first-cousin are called your “first-cousins-once-removed”, and their children are your “first-cousins-twice-removed”, and so on:

To see where your second-cousins come from, we have to move one more level up. Your grandparents’ siblings are your great-aunts and great-uncles. So their children (ie, your parents’ cousins) are your first-cousins-once-removed. And their children are your second-cousins:

The same pattern continues upwards for all earlier generations. Once again, your n^th cousins share your (n + 1)-level ancestors, but not your n^th-level ancestors. Siblings of your n^th-level ancestors are your great-...-great aunts and great-...-great uncles, where “great” is repeated n − 1 times. Furthermore, the n^th cousins of your m^th-level ancestors, and also the m^th-level descendants of your n^th cousins, are your n^th cousins m times removed.

For example, with n = 3 and m = 2, this says that your grandparents’ third-cousins are your third-cousins-twice-removed, and your third-cousins’ grandchildren are also your third-cousins-twice-removed. Tracing back to n = 3 gives:

In this diagram, your third-cousin (n = 3) shares two of your great-great-grandparents (level n + 1 = 4 ancestors) but none of your great-grandparents (level n = 3 ancestors). Your great-great-aunt is a sibling of your great-grandmother (n = 3). Your second-cousin-once-removed achieved that designation by being the second cousin (n = 2) of your mother (level m = 1 ancestor), while your third-cousin-once-removed achieved that designation by being the daughter (level m = 1 descendant) of your third cousin (n = 3). Tricky!

Thicker than water

One of the reasons we care about family trees is because of a sense that certain family relations are “more related” to us, and should be assisted and protected and loved on that basis. This attitude presumably has an evolutionary basis: our genes survived through the ages because our ancestors made efforts to help them survive by caring not only for themselves, but for their close relatives too. Indeed, there is an ancient Bedouin Arab saying, “I against my brother, my brothers and me against my cousins, then my cousins and I against strangers”, which nicely illustrates the philosophy of caring most for those who are genetically closest to us.

This raises the question of just how similar our relatives’ genes are to our own. Well, first of all, about 99.9% of our genetic material is common to all humans (yes, even your in-laws), and indeed is what makes us human. Furthermore, some people may share other genes with us just by chance; for example, if I meet a stranger whose eyes are brown just like mine are, that does not necessarily establish that we are close relatives. In addition, there is lots of randomness in how genes are passed on (each individual gets half of their genetic material from their mother and half from their father, but which bits come from which parent is chosen at random and cannot be predicted), so we cannot draw precise conclusions with certainty.

To deal with all of this, we assign to each pair of individuals a relatedness coefficient which represents the expected fraction (ie, the fraction on average) of their genes which are forced to be identical by virtue of their family relationship. This approach averages out all of the randomness, while focusing on genetic similarities specifically due to family connections.

According to this definition, strangers have a relatedness of zero (the smallest possible value). By contrast, your relatedness with yourself is one (the largest possible value). Other relatedness coefficients fall between these two extremes. For example, your relatedness with your mother is 1/2, since you obtain half of your genetic material from her. And your relatedness with your father is also 1/2. By the same reasoning, your relatedness with your child is again 1/2. So far so good:

Next consider your maternal grandmother. She gave half of her genes to your mother, and then your mother gave half of her genes to you. It is possible that the half you took is exactly the same as the half your grandmother gave. It is also possible that the half you took has no overlap at all with the half your grandmother gave. But on average, that is, in expectation, exactly half of the genetic material you took from your mother originated from your maternal grandmother. So, your relatedness coefficient with your grandmother is one-half of one-half, that is, (1/2) × (1/2), or 1/4:

Continuing up the tree, your relatedness with your great-grandmother is one-half of one-half of one-half, that is: (1/2) × (1/2) × (1/2), or 1/8:

(and similarly for “father” instead of “mother” at any level). In general, your relatedness coefficient with your level-n ancestor is 1/2ⁿ.

By the same reasoning, your relatedness coefficient with your level-n descendant is also 1/2ⁿ. So, for example, your relatedness coefficient with your daughter is 1/2; with your granddaughter is 1/4; and with your great-granddaughter is 1/8 (and similarly for “son” instead of “daughter”).

For siblings, the situation is a little bit more complex. Consider first the case of two half-siblings (half-sisters or half-brothers), that is, people who share just one parent. Since they each got half of their genetic material from that one shared parent, their relatedness coefficient is one-half of one-half, that is 1/4:

Regular (full) siblings similarly share 1/4 of their genetic material through their mother, but also share 1/4 of their genetic material through their father. This gives a total relatedness coefficient of 1/4 + 1/4 = 1/2:

(One special case is identical twins, who have identical genes and thus a relatedness coefficient of one. But fraternal twins have relatedness coefficient 1/2, just like other siblings.)

Continuing onward, since your mother and aunt are siblings, they have relatedness coefficient 1/2. Meanwhile, you and your mother have relatedness coefficient 1/2. Putting this together, you and your aunt (or uncle) have relatedness coefficient (1/2) × (1/2) = 1/4:

(and similarly with “aunt” replaced by “uncle”). And, your relatedness coefficient with your niece or nephew is also 1/4.

Then, since your first-cousin has relatedness coefficient 1/2 with your aunt, who in turn has relatedness coefficient 1/4 with you, it follows that you and your first-cousin share relatedness coefficient 1/8:

Now, since your mother and her first-cousin have relatedness coefficient 1/8, and since you have relatedness coefficient 1/2 with your mother, and since your mother’s first-cousin has relatedness coefficient 1/2 with her own child (who is your second-cousin), it follows that your relatedness coefficient with your second-cousin is (1/2) × (1/8) × (1/2) = 1/32:

In general, switching to level-n cousins from level-(n − 1) cousins introduces two new factors of 1/2. Since (1/2) × (1/2) = 1/4, this means that your relatedness coefficient with your level-n cousin is always 1/4 times your relatedness coefficient with your level-(n − 1) cousin. It follows that your relatedness coefficient with your level-n cousin is equal to 1/2²ⁿ⁺¹.

So, your relatedness coefficient with your first cousin is 1/8; with your second cousin is 1/32; with your third cousin is 1/128; and so on.

What about first-cousins-once-removed, and all of that? Well, since you and your first- cousin have relatedness 1/8, and since your first-cousin and their child (your first-cousin- once-removed) have relatedness 1/2, it follows that you and your first-cousin-once-removed have relatedness coefficient (1/8) × (1/2) = 1/16:

The pattern continues, with each new “removed” introducing an extra factor of 1/2 into the product. It follows that your relatedness coefficient with your nth cousin, m times removed, is equal to 1/2^2n+m+1. For example, your relatedness coefficient with your third cousin (n = 3) twice removed (m = 2) is equal to 1/2⁶⁺²⁺¹ = 1/2⁹ = 1/512 – not very close at all.

We can summarise the relatedness coefficients of various relationships in a table:

This table can be thought of as indicating your level of evolutionary imperative to protect and assist your various relatives. That perspective was nicely summarised by the early evolutionary biologist J.B.S. Haldane, when he was asked if he would give his life to save a drowning brother, and replied “No, but I would to save two brothers or eight cousins.” He was merely observing that 2 × (1/2) = 8 × (1/8) = 1, i.e. that two brothers, or eight cousins, are each “equal” (in evolutionary terms) to one copy of yourself.

So what about that saying, “I against my brother, my brothers and me against my cousins, then my cousins and I against strangers”? Well, in the context of relatedness coefficients, it corresponds to the observation that your relatedness coefficient is higher with yourself (1) than with your brother (1/2), higher with your brother (1/2) than with your first-cousin (1/8), and higher with your first-cousin (1/8) than with a stranger (0). That is:

1 > 1/2 > 1/8 > 0.

Different life forms can lead to different mathematics: eg, in many species of bees and ants the males have only half as much genetic information as females. You can read more about the intricacies of bee relationships in the appendix!

It seems that those Bedouins knew their inequalities well!

Families of all shapes and sizes

Of course, the evolutionary imperative associated with relatedness coefficients does not tell the whole story. You would (hopefully) protect your spouse over your second-cousin even though, strictly speaking, your relatedness coefficient with your spouse is zero (since you have no actual blood relationship). And, parents of adopted children should surely treat them just like biological children, despite the lack of true genetic connection.

Other family relationships can arise too. For example, if you marry, then your spouse’s relations become your corresponding in-law relations – your husband’s father is your father- in-law, your husband’s cousin is your cousin-in-law, and so on. The suffix “in-law” is also used for those who marry your relations – for example, your brother’s wife is your sister-in- law. (One exception is that your aunt’s husband gets to be called your uncle, even though he is “really” your uncle-in-law; and similarly your uncle’s wife gets to be called your aunt.)

Meanwhile, a woman who marries your father after your mother becomes your step-mother (or step-father, if the genders are reversed). Her relations become your corresponding step-relations – your father’s second wife’s brother is your step-uncle, and his children are your step-cousins, and so on. Of course, your genetic relatedness coefficient with your in-laws and your step-relations is zero, since your relationship is through marriage rather than actual blood lines.

Family relations can lead to unexpected surprises. At a recent large family reunion, I met a young man whom I did not know. After some discussion, we determined that my great-grandfather was the brother of his great-grandmother – making us third cousins. Furthermore, my great-grandmother was the sister of his great-grandfather, too. That is, three generations earlier, a brother-and-sister pair had married off with a sister-and-brother pair. This meant that he and I were third-cousins by each of two different paths – we were “double third-cousins”! It followed that our relatedness coefficient was twice that of usual third-cousins – that is, equal to 2 × (1/128) = 1/64 – still not very close, but interesting nonetheless. I wish I had had the presence of mind to immediately say to him, “Pleased to meet you, double-third-cousin. I am honoured to share one sixty-fourth of your genes.”